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Deriving a multilevel circuit

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Consider the function in the attached file- the cost of the minimal SOP expression is 14, which includes four gates and 10 inputs to the gates. Use Shannon's expansion to derive a multilevel circuit that has a lower cost and give the cost of your circuit.

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The solution below explains how Shannon derives her multilevel circuit, using the cost of the minimal SOP expression and gates.

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To find the minimum cost, we have to expand about every variable and then pick the lowest cost ...

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